We have solved the Kohn-Sham Hamiltonian using pseudo-potentials (pp) and planewave basis sets as implemented in Quantum ESPRESSO (QE) density-functional theory (DFT) package [1]}. The exchange-correlation potential of the above Hamiltonian is approximated by PBE-GGA functional [2]} through optimized norm-conserving Vanderbilt pp [3]}. The kinetic energy cutoff for the planewave is taken as 80 \(Ry\) . Gaussian smearing of 0.005 \(Ry\)  is used both for the self-consistent (SC) and non-self-consistent (NSC) calculations. A tight energy threshold of \(10^{-8} Ry\)  has been set for the SC total energy calculations . The functionalized MXene sheets are sufficiently isolated from each other by vacuum (\(c\)  lattice constant = 20 Å) in order to allow negligible interaction between the periodic units. The atomic positions and the in-plane lattice of all the structures have been fully relaxed. The magnetic ground states of every combination of 3d transition metals and the functional groups are predicted from the collinear spin-resolved calculations. Further, the dynamical stability of all the AHE-investigated (ferromagnetic) systems is examined through density functional perturbation theory (DFPT) calculations.
